In many places in the Tanach Hashem uses a name twice (ie Avraham, Avraham in Breshit 22:11; Jacob Jacob in Breshit 46:2; Shmuel shmuel in Shmuel Aleph 3:10 and more).
Rashi says that this is an expression of affection.
With all due respect to Rashi I am not entirely happy with that answer. If it is an expression of affection why isn't it used more? If it is an expression of affection why at these times specifically?
As well, on a related note the call is often answered with Hinneni (commonly translated as Here I am).
Rashi explains that Hinneni is an expression of modesty and eagerness.
Again with all due respect to Rashi, why does this follow the expression of affection? How do the double name calling and the Hinneni relate?